We are trying hard to prop up the government of Hamid Karzai, who is a very corrupt person. For example, Karzai essentially stole the last election. When he was accused of that, he got really angry at the international community and accused them of being out to get him. Then he got rid of the election observers.
We are trying to prop his government up by sending way more troops into fight the Taliban. We want to get the Taliban out of various areas and then hold those areas long enough for the government to take control of them.
We also have to be worried about all the drug production and drug money that is flowing around in Afghanistan, helping support the Taliban and corrupt the national government.
America has recently "doubled down" in that country, sending an additional surge of 35,000 troops. Afghanistan, to be clear, is not really a country at all, but an artificial border around a series of tribes, many of which speak different languages and do not get along well.
The government of Hamid Karzai, a former warlord, is corrupt and tainted, some say hopelessly so, and it appears they just cheated in the last election.
Economically, the country is very poor. The per capita income is in the range of $200 per year per worker. The entire country has but one interstate highway. In conditions like these, it is pretty easy for the Taliban, the group that is fighting us for control, to find recruits.
Osama bin Laden and some of his al-Qaeda forces reportedly move back and forth across the border between Pakistan and Afghanistan, in the high rugged mountains where our forces cannot easily go.
Right now the US military, led by Marines, are invading strongholds in the southern part of the country, where the Taliban started and where it is most popular. The Marines, part of the surge, are currently preparing to take the largest city in the region and the largest one still under Taliban control, Kandahar, with nearly 500,000 people.
It is a guerrilla war, which makes it difficult to win. Our enemy often runs away when we come close and returns as soon as we've left. They are using heroin sales to finance the war, so another of our objectives is to destroy this source of income for them.